Existence of Solutions and Dynamical Models of Chandrasekhar H-Equations

A variety of linear transport equations may be solved in terms of a scattering function,which itself is expressible as a product of so-called H-functions.These functions,first introduced by S. Chandrasekhar [1],satisfy nonlinear integral equations of the form 1 $$H\left( \mu \right) = 1 + \mu H\left( \mu \right)\int_0^1 {\frac{{\psi \left( {\mu '} \right)}}{{\mu + \mu '}}H\left( {\mu '} \right)d\mu '} ,$$ where ß/i(µ) is a characteristic function. It is well known that this equation does not have a unique solution. However, the physical solution of (1) is subject to constraints at the zeroes of the dispersion function. Chandrasekhar [2] provided a solution formula with constants depending upon the roots of a characteristic equation,although such roots are difficult to calculate.